Unable to 'learn' a rotational angle by parametrising the angle as a neural network layer
There are two basic problems with your code:

The functions sin(t) and cos(t) (both in numpy and tensorflow) take radians as inputs. Seeing Constant(90) in your code, and the learning rate of 1. I'm guessing that you assume that it is in degrees - that's incorrect.

In your training data y_ta is not a rotation of y_in:
y_in = np.array([np.sin(t), np.cos(t)]).T
y_ta = np.array([np.cos(t), np.sin(t)]).T



It is a reflection about y=x diagonal. No wonder it fails to find an appropriate rotation.
I just had to change y_ta to:
  y_ta = np.array([-np.cos(t), np.sin(t)]).T

And train with more sensible learning rate:
  model.compile(tf.keras.optimizers.SGD(lr=0.1), loss='MSE')
  model.fit(y_in, y_ta, epochs=10)

To get the angle (which I then convert to degrees):
  (180 * model.layers[0].kernel[0,0].numpy() / np.pi) % 360
  &gt; 90.00187079311581